Visualisation of high-dimensional data

Visualisation of high-dimensional data

Laurent Gatto                      Computational Biology
https://lgatto.github.io           de Duve Institute, UCLouvain
laurent.gatto@uclouvain.be         @lgatt0

Slides: http://bit.ly/highdimvis
Source: https://github.com/lgatto/visualisation

Introduction

• Unsupervised machine learning (clustering): make use of the data to identify patterns of interest.
• Supervised machine learning (classification and regression): use prior knowledge (such as known labels about a subset of the data) to infer new information (labels) for the unlabelled or new data.

From data

To visualisation, annotation and results

Content

• Data
• Hierarchical clustering
• Dimentionality reduction: PCA
• Dimentionality reduction: t-SNE

Proteomics examples

Sample-level visualisations using data from Mulvey et al. (2015) Dynamic Proteomic Profiling of Extra-Embryonic Endoderm Differentiation in Mouse Embryonic Stem Cells.

Protein-level visualisations using data from Christoforou et al. (2016) A draft map of the mouse pluripotent stem cell spatial proteome.

Hierarchical clustering

Hierarchical clustering methods start by calculating all pairwise distances between all features (or samples) and then clusters/groups these based on these similarities. There are various distances measures and clustering algorithms that can be used.

Plots prepared with dist and hclust from the stats package and mrkHClust from pRoloc.

Dimensionality reduction

When the data span over many dimensions (more than 2 or 3, up to thousands), it becomes impossible to easily visualise it in its entirety. Dimensionality reduction techniques such as PCA or t-SNE will transform the data into a new space that summarise properties of the whole data set along a reduced number of dimensions. These are then used to visualise the data along these informative dimensions or perform calculations more efficiently.

Principal Component Analysis

Principal Component Analysis (PCA) is a technique that transforms the original n-dimentional data into a new data space. Along these new dimensions, called principal components, the data expresses most of its variability along the first PC, then second, …. These new dimensions are linear combinations of the orignal data.

Figures produces with plot2D function from the pRoloc package.

t-Distributed Stochastic Neighbour Embedding

t-Distributed Stochastic Neighbour Embedding (t-SNE) is a non-linear dimensionality reduction techique, i.e. that different regions of the data space will be subjected to different transformations. t-SNE will compress small distances, thus bringing close neighbours together, and will ignore large distances.

Figures produces with plot2D function from the pRoloc package.

Parameter tuning

t-SNE (as well as many other methods, in particular classification algorithms) has two important parameters that can substantially influence the clustering of the data

• Perplexity: balances global and local aspects of the data.
• Iterations: number of iterations before the clustering is stopped.

It is important to adapt these for different data.

License

This material is made available under the Creative Commons Attribution license.

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